Counter argument: "boy girl" and "girl boy" are the same option, since there's no reason to distinguish by birth order (or any characteristic other than gender).
I think it would be correct to say that there are 3 possible options: "both boys", "both girls", and "one of each". Since the "both girls" option is impossible, you are left with only two possible options: "both boys", or "one of each". Answer: 1/2
You'd think so, but no, you're still wrong. Think of it this way: Before even filtering out the option with two girls: you have four possible permutations: BB, BG, GB and GG; each of them has a chance of 1/4.
It's twice as likely to have a boy and a girl as to have either two boys or two girls. Put differently: there's a 50/50 chance that the genders match.
If you now remove one of the options (two girls), you're still left with a 2 in 3 chance that they're one boy and one girl.
You can even do an experiment: Write a simple program that does coin tosses, and repeatedly throw pairs of two coins. Then pick one side and filter out all the results where both coins landed on that side. You'll roughly end up with two thirds of the pairs being different sides.
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Counter argument: "boy girl" and "girl boy" are the same option, since there's no reason to distinguish by birth order (or any characteristic other than gender).
I think it would be correct to say that there are 3 possible options: "both boys", "both girls", and "one of each". Since the "both girls" option is impossible, you are left with only two possible options: "both boys", or "one of each". Answer: 1/2
You are correct, and that's what I mean, this question is left for open interpretation. You could literally interpret in multiple ways.
You'd think so, but no, you're still wrong. Think of it this way: Before even filtering out the option with two girls: you have four possible permutations: BB, BG, GB and GG; each of them has a chance of 1/4.
It's twice as likely to have a boy and a girl as to have either two boys or two girls. Put differently: there's a 50/50 chance that the genders match.
If you now remove one of the options (two girls), you're still left with a 2 in 3 chance that they're one boy and one girl.
You can even do an experiment: Write a simple program that does coin tosses, and repeatedly throw pairs of two coins. Then pick one side and filter out all the results where both coins landed on that side. You'll roughly end up with two thirds of the pairs being different sides.